Extruding straight down
Immediately after typing E (extrude), type Z twice: first to override the default direction (along the faces' normal), then to constrain the extrusion along the Z axis.



&nbsp;&nbsp;&nbsp;&nbsp;(E, Z, Z, move, Enter. Note "along global Z" on the bottom bar)



To add on this: you can constrain to an axis - X, Y or Z - also the other familiar operations G (move), R (rotate) and S (scale). 

Similarly, Shift+Z constrains the transformation to all axes except Z. 

Finally, selecting an axis twice means that the axis local to the object's internal coordinates is used, rather than the global one.